Do rock music CDs and country music CDs give the consumers the same amount of music listening time? A sample of 12 randomly selected single rock music CDs and a sample of 14 randomly selected single country music CDs have the following total lengths (in minutes).

Assume that the two populations are normally distributed with equal standard deviations.
a. Compute the value of the test statistic t for testing the null hypothesis that the mean lengths of the rock and country music single CDs are the same against the alternative hypothesis that these mean lengths are not the same. Use the value of this t statistic to compute the (approximate) p-value.
b. Compute the value of the (one-way ANOVA) test statistic F for performing the test of equality of the mean lengths of the rock and country music single CDs and use it to find the (approximate) p-value.
c. How do the test statistics in parts a and b compare? How do the p-values computed in parts a and b compare? Do you think that this is a coincidence, or will this always happen?

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Rock Music 43.0 44.3 63.8 32.8 54.2 51.3 64.8 36.1 33.9 51.7 36.5 59.7 Country Music 45.3 40.2 42.8 33.0 33.5 37.7 36.8 34.6 33.4 36.5 43.3 31.7 44.0 42.7